Corollary 1
Tag 06SQ, permanent. Cite it as [Bourbaki, Tag 06SQ].
Algebra, chapter V, § 14. Transcendental extensions
— If E and F are linearly disjoint, then E is algebraically disjoint from F over K. Conversely, if E is a pure extension of K and is algebraically disjoint from F over K, then E and F are linearly disjoint over K.
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.
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